Internal instability is a form of internal erosion in broadly-graded cohesionless soils in which fine particles can be eroded at lower hydraulic gradients than predicted by classical theory for piping or heave. A key mechanism enabling internal instability is the formation of a stress-transmitting matrix dominated by the coarse particles that leaves the finer particles under lower effective stress. In this study discrete element modeling is used to analyze the fabric and effective stress distribution within idealized gap-graded samples with varying potential for internal stability. The reduction in stress within the finer fraction of the materials is directly quantified from grain-scale data. The particle size distribution, percentage finer fraction and relative density are found to influence the stress distribution. In particular, effective stress transfer within a critical finer fraction between 24% and 35% is shown to be highly sensitive to relative density.

The internal stability of a soil is a measure of its susceptibility to suffusion and suffosion, two forms of internal erosion. The internal stability of granular filters must be carefully considered when designing new embankment dams and assessing the risk associated with existing embankment dams. Current guidelines for assessing the internal stability of such filters were empirically derived from macroscale observations and consider the shape of the particle-size distribution curve. These guidelines lack a fundamental, scientific micromechanical basis. The initiation and propagation of internal erosion is clearly a particlescale phenomenon, and this paper applies particulate mechanics to provide a micromechanical justification for one currently used stability criterion. The study used discrete element simulations of idealised virtual soil samples that had various degrees of internal stability when assessed using the criterion proposed by Kézdi [10]. The internal topologies of stable and unstable samples were analysed by considering the distributions of inter-particle contact forces, the number of particle-particle contacts and the average particle stresses. Clear correlations are observed between the filter stability criterion and the average number of contacts per particle and the probability that a given particle participates in stress transmission. The phenomenon of a critical fines content, at which the existing guidelines are no longer considered to be valid, is also considered.

This paper considers factors influencing the fabric of bimodal or gap-graded soils. Discrete element method simulations were carried out in which the volumetric fines content and the size ratio between coarse and fine particles were systematically varied. Frictionless particles were used during isotropic compression to create dense samples; the coefficient of friction was then set to match that of spherical glass beads. The particle-scale data generated in the simulations revealed key size ratios and fines contents at which transitions in soil fabric occur. These transitions are identified from changes in the contact distributions and stress-transfer characteristics of the soils and by changes in the size of the void space between the coarse particles. The results are broadly in agreement with available experimental data on minimum void ratio and contact distributions. The results have implications for engineering applications including assessment of the internal stability of gap-graded soils in embankment dams and flood embankments. Keywords Gap-graded soil • Internal instability • Discrete element method • Partial coordination numbers • Void size This article is part of the Topical Collection on Micro origins for macro behavior of granular matter.

The retention capability of granular filters is controlled by the narrow constrictions connecting the voids within the filter. The theoretical justification for empirical filter rules used in practice includes consideration of an idealised soil fabric in which constrictions form between co-planar combinations of spherical filter particles. This idealised fabric has not been confirmed by experimental or numerical observations of real constrictions. This paper reports the results of direct, particle-scale measurement of the constriction size distribution (CSD) within virtual samples of granular filters created using the discrete-element method (DEM). A previously proposed analytical method that predicts the full CSD using inscribed circles to estimate constriction sizes is found to poorly predict the CSD for widely graded filters due to an over-idealisation of the soil fabric. The DEM data generated are used to explore quantitatively the influence of the coefficient of uniformity, particle size distribution and relative density of the filter on the CSD. For a given relative density CSDs form a narrow band of similarly shaped curves when normalised by characteristic filter diameters. This lends support to the practical use of characteristic diameters to assess filter retention capability.

This contribution considers the critical time increment (〖∆t〗_crit) to achieve stable simulations using particulate discrete element method (DEM) codes that adopt a Verlet-type time integration scheme. The 〖∆t〗_crit is determined by considering the maximum vibration frequency of the system. Based on a series of parametric studies, 〖∆t〗_crit is shown to depend on the particle mass (m), the maximum contact stiffness (Kmax), and the maximum particle coordination number (CN,max). Empirical expressions relating 〖∆t〗_crit to m, Kmax, and CN,max are presented; while strictly only valid within the range of simulation scenarios considered here, these can inform DEM analysts selecting appropriate 〖∆t〗_crit values

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In particulate geomechanics it is common to quantify fabric anisotropy using contact and particle orientations. Measurement of void anisotropy is less common, most likely owing to the difficulties associated with defining individual voids. Here a Delaunay tessellation-based approach is applied to measure anisotropy of the inter-void constriction orientations. This new measure of fabric anisotropy was capable of identifying stress-induced anisotropy in discrete-element modelling true triaxial simulations with spherical particles. A relationship is established between the constriction orientations, the macro-scale principal stress directions and the micro-scale contact normal orientations.

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